A kinematic mount is a coupling of two mechanical components (referred to in this application as A and B) that constrains all and only the possible degrees of freedom between them. For the case of two free rigid bodies in three dimensions, there are six degrees of freedom between them. When components are kinematically coupled, the coupling is stress-free and repeatable.
Kinematic couplings are old art. For example, if component A has three spherical protrusions, and component B has a flat area, a conical depression, and a V-groove depression, and if the spherical protrusions of component A fit onto the features of component B, then there is only one spatial relation between the components under which the spherical protrusions are tangent to the features of component B, and a kinematic mount is formed—the conical depression eliminates three degrees of freedom, the V-groove eliminates two degrees of freedom, and the flat area eliminates the last of the 6 degrees of freedom. This mount is commonly known as a 3-2-1 mount, or a cone-V-flat mount. (The term “3-2-1” is also sometimes used to refer to a three-sided kinematic mount consisting of six points—this is not what this description refers to.)
A similar scheme is the 2-2-2 mount, in which three spherical protrusions in component A fit into three V-groove depressions in component B, eliminating 2 degrees of freedom each. This mount is called a three-groove mount. It has an advantage over the 3-2-1 mount in that its three component mates are identical, and so the mount is symmetrical.
It is important to note that the precise location of the features does not matter—as long as the protrusions fall anywhere within their respective mating feature, the mount will be kinematic. This means that there is no need to require tight manufacturing tolerances to achieve the stress-free, repeatable, and rigid coupling. The tolerances on the shape of the individual mounting features (spheres, cone, V-groove, flat) are assumed to be much tighter than the positional tolerances of the features and so is assumed to be perfect. For example, the cone is assumed to touch the sphere along a circle (whereas an imperfect cone would touch the sphere in three points.) This is a practical assumption, since it is relatively easy to achieve these tolerances.
For the same reason, changes in the geometry caused by thermal expansion do not affect the kinematicity of the mount—the components are not over-constrained, and while their spatial relationship may shift, no internal stresses will develop.
A common issue with kinematic mounts is that they often involve point contacts, as in the contact between a spherical protrusion and a V-groove. Point contacts are limited in the amount of load they can hold. Beyond a certain limit, the stress concentration permanently deforms the mating surfaces, and the deformed parts no longer function properly.
In U.S. Pat. Nos. 6,729,589 and 7,173,779 is described a mating body geometry comprised of spherical and cylindrical surfaces that interface a V-groove and a conical depression without creating point contacts, only line contacts. The bodies can then be used in either a cone-V-flat or a three groove mount, greatly increasing their load capacities. The V-groove is more difficult to machine, since it is not a feature of rotation.